Problem 202 - A Complete Resource Book in Chemistry for JEE Main

Question

The standard reduction potentials for \(\mathrm{Zn}^{2+} / \mathrm{Zn}, \mathrm{Ni}^{2+} / \mathrm{Ni}\), and \(\mathrm{Fe}^{2+} / \mathrm{Fe}\) are \(-0.76,-0.23\) and \(-0.44 \mathrm{~V}\) respectively. The reaction \(\mathrm{X}+\mathrm{Y}^{2+} \rightarrow \mathrm{X}^{2+}+\mathrm{Y}\) will be spontaneous when (a) \(\mathrm{X}=\mathrm{Fe}, \mathrm{Y}=\mathrm{Zn}\) (b) \(\mathrm{X}=\mathrm{Ni}, \mathrm{Y}=\mathrm{Zn}\) (c) \(\mathrm{X}=\mathrm{Ni}, \mathrm{Y}=\mathrm{Fe}\) (d) \(\mathrm{X}=\mathrm{Zn}, \mathrm{Y}=\mathrm{Ni}\)

Step-by-Step Solution

Answer

The reaction is spontaneous for case (d): \(\mathrm{X} = \mathrm{Zn}\) and \(\mathrm{Y} = \mathrm{Ni}\).

Step 1: Understanding Spontaneity

For a redox reaction to be spontaneous, the cell potential \(E^0_{cell}\) must be positive. The reaction \(\mathrm{X} + \mathrm{Y}^{2+} \rightarrow \mathrm{X}^{2+} + \mathrm{Y}\) is spontaneous if the reduction potential of \(\mathrm{Y}^{2+} / \mathrm{Y}\) is greater than that of \(\mathrm{X}^{2+} / \mathrm{X}\), because \(\mathrm{Y}^{2+}\) is reduced and \(\mathrm{X}\) is oxidized.

Step 2: Checking Each Case

We will check each given case to find the pair that results in a positive cell potential. This means we need to consider the potential difference, \(E^0_{cell} = E^0_{cathode} - E^0_{anode}\), where the cathode is \(\mathrm{Y}^{2+}/\mathrm{Y}\) and the anode is \(\mathrm{X}/\mathrm{X}^{2+}\).

Step 3: Case (a) Evaluation

For case (a), \(\mathrm{X} = \mathrm{Fe}\) and \(\mathrm{Y} = \mathrm{Zn}\): - \(E^0_{\mathrm{Zn}^{2+}/\mathrm{Zn}} = -0.76 \, \mathrm{V}\)- \(E^0_{\mathrm{Fe}^{2+}/\mathrm{Fe}} = -0.44 \, \mathrm{V} \)Hence, \(E^0_{cell} = -0.76 - (-0.44) = -0.32 \, \mathrm{V}\). This potential is negative, so the reaction is not spontaneous.

Step 4: Case (b) Evaluation

For case (b), \(\mathrm{X} = \mathrm{Ni}\) and \(\mathrm{Y} = \mathrm{Zn}\): - \(E^0_{\mathrm{Zn}^{2+}/\mathrm{Zn}} = -0.76 \, \mathrm{V}\)- \(E^0_{\mathrm{Ni}^{2+}/\mathrm{Ni}} = -0.23 \, \mathrm{V}\)Thus, \(E^0_{cell} = -0.76 - (-0.23) = -0.53 \, \mathrm{V}\).This potential is negative, so the reaction is not spontaneous.

Step 5: Case (c) Evaluation

For case (c), \(\mathrm{X} = \mathrm{Ni}\) and \(\mathrm{Y} = \mathrm{Fe}\):- \(E^0_{\mathrm{Fe}^{2+}/\mathrm{Fe}} = -0.44 \, \mathrm{V}\)- \(E^0_{\mathrm{Ni}^{2+}/\mathrm{Ni}} = -0.23 \, \mathrm{V} \)So, \(E^0_{cell} = -0.44 - (-0.23) = -0.21 \, \mathrm{V}\).This potential is negative, so the reaction is not spontaneous.

Step 6: Case (d) Evaluation

For case (d), \(\mathrm{X} = \mathrm{Zn}\) and \(\mathrm{Y} = \mathrm{Ni}\):- \(E^0_{\mathrm{Ni}^{2+}/\mathrm{Ni}} = -0.23 \, \mathrm{V}\)- \(E^0_{\mathrm{Zn}^{2+}/\mathrm{Zn}} = -0.76 \, \mathrm{V}\)Therefore, \(E^0_{cell} = -0.23 - (-0.76) = 0.53 \, \mathrm{V} \).This potential is positive, so the reaction is spontaneous.

Key Concepts

Standard Reduction Potential

Standard reduction potential is a measure of the tendency of a chemical species to gain electrons and thereby be reduced. Each half-cell in a redox reaction has a standard reduction potential associated with it, denoted as \(E^0\). The values are measured in volts under standard conditions, which include a temperature of 25°C, a 1 M concentration for each ion participating in the reaction, and a pressure of 1 atm for gases.

More positive \(E^0\) values indicate a stronger ability to gain electrons, thus acting as a good oxidizing agent. Conversely, a more negative \(E^0\) means that the species is more likely to lose electrons, acting as a reducing agent. Understanding this concept is crucial when predicting whether a given redox reaction will occur spontaneously. By looking at the standard reduction potentials of the half reactions, one can determine which species will be reduced and which will be oxidized.

Spontaneous Reactions

For a chemical reaction to be spontaneous, it must result in a net release of energy. In electrochemistry, this is represented by a positive cell potential \(E^0_{cell}\). The cell potential can be calculated by finding the difference between the standard reduction potentials of the two half-reactions: the cathode and the anode.

The formula for determining whether a redox reaction is spontaneous is: \[E^0_{cell} = E^0_{cathode} - E^0_{anode}\] Where the cathode undergoes reduction and possesses a higher reduction potential compared to the anode, which undergoes oxidation. For a reaction to be spontaneous, \(E^0_{cell}\) should be greater than zero. This indicates that electrons will move from the anode to the cathode naturally, without the need for external energy.

Redox Reactions

Redox reactions, short for reduction-oxidation reactions, involve the transfer of electrons between two chemical species. In these reactions, one species is oxidized (loses electrons) and another is reduced (gains electrons). Understanding who the oxidizing and reducing agents are is pivotal to comprehending how these reactions occur.

In any redox reaction, the total number of electrons lost in oxidation must equal the number of electrons gained in reduction to maintain charge balance. The oxidative strength and reductive strength are determined by the standard reduction potentials discussed earlier.

• The species with the higher reduction potential is reduced.
• The species with the lower reduction potential is oxidized.

By understanding and calculating the conditions under which redox reactions are spontaneous, students can better predict chemical behavior and improve their grasp of electrochemical applications.